I'm a bit "GC hater" so obviously I'm heavily biased but to me it just means that GC make it easier to write sloppy, poorly architectured code where you have a mess of a data-dependency graph and nobody knows who owns what and when things need to be deleted, so you let the GC (hopefully) figure it out. In my experience this leads to all sorts of issues independently of memory management, such as having obsolete data lingering in certain parts of the program because it's not expunged properly.
IMO GC or not having clear ownership semantics are necessary to properly architecture anything more complicated than a script. And if you have ownership semantics then why do you need a GC anyway?
Ownership is not a fundamental architectural property - it is "only" a powerful technique for tracking data with a specific lifetime (of course, even in GC languages you still need proper ownership semantics for some pieces of data).
That's why Java and C# both had to introduce a way of (semi-)automatically closing resources, waiting for the GC was a catastrophe.
Java and C# did nothing new there, only catching up with was already the state of the art before they were born.
The basic assumption with a GC'ed language is that the lifetime ends once the object isn't referenced anymore. You rarely have to deal with it at all, so those "logic errors" happen much less frequently.
If we look at the major real-world languages without GC (C/C++), it is your job to figure out the lifetime. You will fuck this up unless you structure your program in very disciplined way and that's frankly too much to ask of the vast majority of programmers.
In other words the DAG would never be traversed to allocate or free memory, each vertex would be held by a vector or other container and the edges represented by an adjacency list/matrix.
It's faster and safer than pointer chasing.
No, it solves the problem because resource lifetime is no longer a concern. A field advances as we decrease the number of irrelevant details we need to attend to.
Turns out, most of the time, memory is one such concern. You can argue that we need better approaches when memory is a concern, but that doesn't discount the value of GC as the right default.